`f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1` is continuous in the interval `[-1,1],` then `p` is equal to `-1` (b) `-1/2` (c) `1/2` (d) 1

Options

A. `-1`
B. `-1//2`
C. `1//2`
D. `1`

Answer

B

Explanation

It is given that f(x) is a continous in [-1,1]. Therefore, it is also continous at x=0
`therefore underset(x-0^(-))lim f(x)=lim(xto 0^(+))f(x)=f(0)`
`Rightarrow underset(x to 0)lim (sqrt(1+pi)-sqrt(1-px))/(x) underset(x to 0)lim (2x+1)/(x-2)=(2xx0+1)/(0-2)`
`Rightarrow underset(x to 0)lim (2px)/((sqrt(1+pi)-sqrt(1-px)))=-(1)/(2)`
`Rightarrow underset(x to 0)lim (2p)/(sqrt(1+pi)-sqrt(1-px))=-(1)/(2)Rightarrowp=-(1)/(2)`